• 대한수학회보
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• 제43권2호
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• pp.293-297
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• 2006

Using the concept of codes on ordered sets introduced by Brualdi, Graves and Lawrence, we consider perfect codes on the ordinal sum of two ordered sets, the standard ordered sets and the disjoint sum of two chains.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.825-838
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• 2021

In this paper the concept of ordered fuzzy filters is introduced in Heyting almost distributive lattices and the properties of these ordered fuzzy filters are studied. We characterized and proved a set of theorems of ordered fuzzy filters. Some topological properties of prime ordered fuzzy filters are also studied.

• 충청수학회지
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• 제25권1호
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• pp.105-113
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• 2012

Generalizing modular lattices, a concept of modular ordered sets was introduced by Chajda and Rachunek. In this paper, we characterize modular ordered sets as those partially ordered set P satisfying that for $a,\;b,\;c\;{\in}\;P\;with\;b\;{\leq}\;c,\;l(a,\;b)\;=\;l(a,\;c)\;and\;u(a,\;b)\;=\;u(a,\;c)$ imply $b\;=\;c$. Using this, we obtain a sufficient condition for them. We also discuss the modularity of the Dedekind-MacNeille completions of ordered sets.

• 대한수학회보
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• 제37권4호
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• pp.685-690
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• 2000

In this paper, we consider the jump number of the split P[S] of a subset S ordered set P. $For\ x\in\ P,\ we\ show\ that\ s(P)\leq\ s(P[x]\leq\ s(P)+2$ and give a necessary and sufficient condition for which s(P[x])=s(P).

• 대한수학회보
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• 제28권2호
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• pp.243-254
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• 1991

For a given function f.mem.F and a set of functions J.subeq.F, the problem of isotonic optimization is to determine an element in the set nearest to f in some sense. Specifically, let X be a partially ordered finite set with a partial order << and, let F"=F(X) be the linear space of all bounded real valued functions on X. A function g.mem.F is said to be an isotonic function if g(x).leq.g(y) whenever x,y.mem.X and x << y.<< y.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.525-535
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• 2016

We define a fuzzy lattice as a fuzzy relation, prove the distributive inequalities and the modular inequality of fuzzy lattices, and show that the fuzzy totally ordered set is a distributive fuzzy lattice and that the distributive fuzzy lattice is modular.

• 충청수학회지
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• 제7권1호
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• pp.13-23
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• 1994

In this paper, we consider the higher-order type theoretic language L and construct a type model D of complete partial ordered set. We show that the complete partial ordered set for the language L gives rise to a category and generates a topos.

• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.563-573
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• 2000

In this thesis, we propose the test statistic for ordered alternatives on c-sample ranked set samples(RSS). The proposed test statistic JRSS is Jonckheere type statistic using the median of the i-th samples in each cycle. We obtained the asymptotic property of the proposed test statistic and the asymptotic relative efficiencies of the proposed test statistic with respect to J SRS which Jonckheere type statistic on simple random samples(SRS). From the simulation works, J RSS is superior to J SRS. We compared the empirical powers of J RSS with respect to U RSS on ranked set sample and U SRS on simple random sample using all samples, which are proposed by Kim, Kim and Lee(1999). The powers of J RSS are nearly the same values when entire sample size is large. J RSS is superior to U RSS. J RSS is simpler than U RSSon calculating process.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.657-668
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• 2016

Given a partition ${\lambda}=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_l)$ of a positive integer n, let Tab(${\lambda}$, k) be the set of all tabloids of shape ${\lambda}$ whose weights range over the set of all k-compositions of n and ${\mathcal{OP}}^k_{\lambda}_{rev}$ the set of all ordered partitions into k blocks of the multiset $\{1^{{\lambda}_l}2^{{\lambda}_{l-1}}{\cdots}l^{{\lambda}_1}\}$. In [2], Butler introduced an inversion-like statistic on Tab(${\lambda}$, k) to show that the rank-selected $M{\ddot{o}}bius$ invariant arising from the subgroup lattice of a finite abelian p-group of type ${\lambda}$ has nonnegative coefficients as a polynomial in p. In this paper, we introduce an inversion-like statistic on the set of ordered partitions of a multiset and construct an inversion-preserving bijection between Tab(${\lambda}$, k) and ${\mathcal{OP}}^k_{\hat{\lambda}}$. When k = 2, we also introduce a major-like statistic on Tab(${\lambda}$, 2) and study its connection to the inversion statistic due to Butler.

• 대한수학회논문집
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• 제22권1호
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• pp.9-14
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• 2007

In this paper, we introduce more extended special sets in implicative semigroups, and obtain some relations with ordered filters.